Phase Transitions In One-dimensional Systems Research Articles

Topological phase transitions with zero indirect band gaps

Topological phase transitions in band models are usually associated to the gap closing between the highest valance band and the lowest conduction band, which can give rise to different types of nodal structures, such as Dirac/Weyl points, lines and surfaces. In this work, we show the existence of a different kind of topological phase transitions in one-dimensional systems, which are instead characterized by the presence of a robust zero indirect gap, which occurs when the top of the valence band coincides with the bottom of the conduction band in energy but not in momentum. More specifically, we consider an one-dimensional model on a trimer chain that is protected by both particle–hole and chiral-inversion symmetries. At the critical point, the system supports a Dirac-like point. After introducing a deforming parameter that breaks both inversion and chiral symmetries but preserves their combination, we observe the emergence of a zero indirect band gap, which results to be related to the persymmetry of our Hamiltonian. Importantly, the zero indirect gap holds for a range of values of the deforming parameter. We finally discuss the implementation of the deforming parameter in our tight-binding model through time-periodic (Floquet) driving.

Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states.

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent β of absorbing phase transitions in systems with two symmetric absorbing states. The value of β was conjectured to be 13/14≈0.93 and Monte Carlo simulation studies in the literature have repeatedly reproduced values consistent with the conjecture. In this paper, we systematically estimate β by analyzing the effective exponent after finding how strong corrections to scaling are. We show that the widely accepted numerical value of β is not correct. Rather, we obtain β=1.020(5) from different models with two symmetric absorbing states.

Resistive asymmetry due to spatial confinement in first-order phase transitions

We report an asymmetry in the $R$ vs $T$ characteristics across the first-order metal-insulator transition (MIT) of ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ nanowires. The resistance changes in a few, large jumps during cooling through the MIT, while it does it in a smoother way during warming. The asymmetry is greatly enhanced as the width of the nanowire approaches a characteristic domain size. Our results, together with previous reports on ${\mathrm{VO}}_{2}$ [W. Fan et al., Phys. Rev. B 83, 235102 (2011)] and FeRh [V. Uhl\'{\i}\ifmmode \check{r}\else \v{r}\fi{} et al., Nat. Commun. 7, 13113 (2016)] imply that asymmetry is a generic feature of first-order phase transitions in one-dimensional systems. We show that this behavior is a simple, elegant consequence of the combined effects of the transition hysteresis and the temperature dependence of the insulating gap in this case (and generically, the order parameter relevant for the physical observable). We conclude that our proposed asymmetry mechanism is universally applicable to many electronic first-order phase transitions.

Erratum to: General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions

We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and subsequently its limited range of applicability. To further underscore this point, we present several examples of one-dimensional short ranged models that exhibit true, thermodynamic phase transitions, with increasing level of complexity and closeness to reality. Thus having made clear the necessity for a result broader than van Hove's theorem, we set out to prove such a general non-existence theorem, widening largely the class of models known to be free of phase transitions. The theorem is presented from a rigorous mathematical point of view although examples of the framework corresponding to usual physical systems are given along the way. We close the paper with a discussion in more physical terms of the implications of this non-existence theorem.

Magneto-elastic phase transitions in one-dimensional systems

The magneto-elastic phase diagram in one-dimensional systems relating to the interplaybetween magnetism and lattice distortion is studied in a double-exchange andsuper-exchange model considering classical localized spins and the limit of large Hund’scoupling. At low super-exchange interaction energy, a phase transition occurs betweenelectron-full ferromagnetic distorted and electron-empty antiferromagnetic undistortedphases via phase separation. In this case, all electrons and lattice distortions are foundwithin the ferromagnetic domain. For higher super-exchange interaction energy,phase separations consisting of two- or three-site distorted independent magneticpolarons separated by electron-empty undistorted antiferromagnetic links areobtained. In this regime, each polaron contains an electron, leading to a Wignercrystallization. The lattice distortion and charge distribution inside the polarons are alsocalculated.

Phase transitions in one dimension: Are they all driven by domain walls?

Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B) the ferromagnetic, spin 1/2 Ising model with long-range pair interactions varying as the inverse square of the distance between pairs. In both cases it can be shown that the domain wall configurations become entropically stable at, or very near, the critical temperature. This might provide a “positive” criterion for the occurrence of a phase transition in one-dimensional systems.

Factorised steady states and condensation transitions in nonequilibrium systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the ‘zero-range process’ and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several ‘condensation’ transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.

Condensation Transitions in Nonequilibrium Systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium- for example phase transitions in one-dimensional systems. In this talk I will review several `condensation' transitions that occur when a conserved quantity is driven through the system. Although the condensation is spatial, i.e. a finite fraction of the conserved quantity condenses into a small spatial region, useful comparison can be made with usual Bose-Einstein condensation. Amongst some one-dimensional examples I will discuss the `Bus Route Model' where the condensation corresponds to the clustering together of buses moving along a bus-route.

General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions

We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and subsequently its limited range of applicability. To further underscore this point, we present several examples of one-dimensional short ranged models that exhibit true, thermodynamic phase transitions, with increasing level of complexity and closeness to reality. Thus having made clear the necessity for a result broader than van Hove's theorem, we set out to prove such a general non-existence theorem, widening largely the class of models known to be free of phase transitions. The theorem is presented from a rigorous mathematical point of view although examples of the framework corresponding to usual physical systems are given along the way. We close the paper with a discussion in more physical terms of the implications of this non-existence theorem.

Effect of hydrostatic pressure on phase transitions in spin-crossover 1D systems

A model is developed to elucidate the role of hydrostatic pressure on the spin-crossover phase transitions in one-dimensional systems. The model involves long-range electron-deformational and short-range interactions. The conditions when pressure suppresses the thermal hysteresis are discussed. The pressure-induced system’s bistability is predicted. The qualitative explanation of experimental data is given.

Phase transitions in one-dimensional nonequilibrium systems

The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We then give an overview of the one-dimensional phase transitions which have been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is known exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We analyse in detail a condensation phase transition in the model and show how conditions under which it may occur may be related to the existence of an effective long-range energy function. It is also shown that even when the conditions for condensation are not fulfilled one can still observe very sharp crossover behaviour and apparent condensation in a finite system. Although the zero-range process is not well known within the physics community, several nonequilibrium models have been proposed that are examples of a zero-range process, or closely related to it, and we review these applications here.

Kinetics of nonequilibrium second-order phase transitions in one-dimensional systems

Kinetics of nonequilibrium second-order phase transitions in one-dimensional systems

The One-Dimensional KDP and Other Ice Rule Models

One-dimensional ice, KDP, F, eight-vertex and general six-vertex models are discussed. As these models cannot be defined uniquely in one dimension, various possibilities are presented. For a particular one-dimensional lattice, the KDP, the eight-vertex and the six­ vertex models undergo a first-order phase transition. The KDP model is considered also in the presence of electric fields. Thermodynamic quantities of the model show unusual behavior. dimensional ice models are discussed. In § 3 the one-dimensional KDP and F models are considered. We will see that only the KDP model with a particular boundary condition for the vertical direction undergoes a first-order phase transition, and that the model is equivalent to Nagle's one-dimensional KDP model. Occur­ rence of a phase transition in one-dimensional systems is briefly discussed. In § 4 the KDP model which has a transition is considered in external electric fields. The careful consideration of the possible ways of defining the one-dimensional KDP models is necessary when we introduce the external fields precisely. It is shown that the transition temperature is increased and the order of the trasition is not changed by the introduction of the fields. The latter fact is a remarkable difference from the result of the two-dimensional KDP model. In § 5 the one­ dimensional eight-vertex model is considered and the possible phase transition is also of first order which differs from the two-dimensional case. Condition for the occurrence of the transition in the general six-vertex model which is a generalization

Incompatibility of BCS pairing and the Peierls distortion in one-dimensional systems. II. Fluctuation effects

The relationship between the BCS superconducting and the Peierls insulating phase transitions in one-dimensional systems is investigated. This is the second in a series of two papers and treats the effects of simultaneous fluctuations in both order parameters. The coefficients appearing in the Landau-Ginsburg free-energy functional are calculated from the mean-field theory results of the first paper (I) and the statistical-mechanical properties are obtained by expressing the partition function as a functional integral over the Landau-Ginsburg free-energy functional. The problem is reduced to solving for the eigenfunctions and eigenvalues of a particular two-dimensional anharmonic oscillator. Results for the fluctuations and correlation lengths of both order parameters are presented both for a narrow-critical-region model, closely related to that examined by Scalapino, Sears, and Ferrell for the case of one order parameter, and for a wide-critical-region model, based on the approach of Lee, Rice, and Anderson (LRA), who also considered only a single order parameter. The conclusions reached in both models are that fluctuations associated with the lower-critical-temperature order parameter are strongly suppressed. In addition, the correlation length of this order parameter does not appear to grow large as the temperature is lowered. These results support those obtained in I: The BCS and Peierls phase transitions are generally incompatible. Several unexpected and possibly unphysical features of the LRA model for one order parameter are also discussed.

Absence of phase transitions in one-dimensional systems with hard cores

Conditions are given under which a one-dimensional classical system undergoes no phase transition.